Mr. Boulton. But, like many English inventions, it never was adequately estimated, until it was brought into public notice by a Frenchman. M. Montgolfier, its re-inventor, gave to it the name which it now bears of the Hydraulic Ram, in allusion to the battering ram.

The essential parts of this machine are represented in the annexed diagram. When the water in the pipe A B (moving

D

in the direction of the arrows) has acquired sufficient velocity, it raises the valve в, which immediately stops its farther passage. The momentum which the water has acquired then forces a portion of it through the valve, c, into the air vessel, D. The condensed air in the upper part of D causes the water to rise into the pipe E, as long as the effect of the horizontal column continues. When the water becomes quiescent, the valve в will open again by its own weight, and the current along A B will be renewed, until it acquires force enough to shut the said valve в, open c, and repeat the operation.

The motion in the horizontal tube arises from the acceleration of the velocity of a liquid mass falling down another tube, and communicating with this.

In an experiment made upon an hydraulic ram, at Avilly, near Senlis, by M. Turquet, bleacher, the expense of power was found to be to the produce, as 100 to 62. In another, as 100 to 55 in two others, as 100 to 57. So that a hydraulic ram, placed not in unfavourable circumstances, may be reckoned to employ usefully rather more than half its force.

*For more full accounts of the three last contrivances, the reader may consult the 2d volume of my Mechanics.

SECTION III.-Wind and Windmills.

1. Air, when in continuous motion in one direction, becomes a very useful agent of machinery, of greater or less energy, according to the velocity with which it moves.

Were

it not for its variability in direction and force, and the consequent fluctuations in its supply, scarcely any more appropriate first mover could generally be wished for. And even with all its irregularity, it is still so useful as to require a separate consideration.

2. The force with which air strikes against a moving surface, or with which the wind strikes against a quiescent surface, is nearly as the square of the velocity: or, more correctly, the exponent of the velocity determined according to the rule given at pa. 103, varies between 2:03 and 2.05; so that in most practical cases, the exponent 2, or that of the square, may be employed without fear of error. If I be the angle of incidence, s the surface struck in feet, and v the velocity of the wind, in feet, per second; then for the force in avoirdupois pounds, either of the two following approximations v2 s2 sin3 I may be used: viz. f =

or f=

440

002288 v2 s2 sin2 1.

Of these, the first is usually the easiest in operation, requiring only two lines of short division, viz. by 40 and by 11. If the incidence be perpendicular, sin2 1 =

1, and these be

come,

f

=

v2 52
440

=002288 va s2.

3. The table in the margin exhibits the force of the wind when blowing perpendicularly upon a surface of one foot square, at the several velocities announced. The velocity of 80 miles per hour is that by which the aeronaut Garnerin was carried in his balloon from Ranelagh to Colchester, in June, 1802. It was a strong and boisterous wind; but did not assume the character of a hurricane, although a wind with. that velocity is so characterized in Rouse's table. In Mr. Green's aerial voyage from Leeds, in September, 1823, he travelled 43 miles in 18 minutes, although his balloon rose to the height of more than 4000 yards.

Borda found by experiment in the year 1762, that the force of the wind is very nearly as the square of the velocity, but

he assigned that force to be greater than what Rouse found (as expressed in the above table) in the ratio of 111 to 100. Borda ascertained also, as was natural to expect, that, upon different surfaces with the same velocity, the force increased more rapidly than the surface. M. Valtz, applying the method of the minimum squares to Borda's results, ascertained that the whole might be represented by the formula

y =

0.001289 x2 +0·000050541 x3

and nearly as correctly by y = 0·00108 aa

2 representing the surface in square inches (French), and y the force corresponding to the velocity of 10 feet per second expressed in French pounds.

4. In the application of wind to mills, whatever varieties there may be in their internal structure, there are certain rules and maxims with regard to the position, shape, and magnitude of the sails, which will bring them into the best state for the action of the wind, and the production of useful effect. These have been considered much at large by Mr. Smeaton for this purpose he constructed a machine, of which a particular description is given in the Philosophical Transactions, vol. 51. By means of a determinate weight it carried round an axis with an horizontal arm, upon which were four small moveable sails. Thus the sails met with a constant and equable blast of air; and as they moved round, a string with a weight affixed to it was wound about their axis, and thus showed what kind of size or construction of sails answered the purpose best. With this machine a great number of experiments were made; the results of. which were as follow:

(1.) The sails set at the angle with the axis, proposed as the best by M. Parent and others, viz. 55°, was found to be the worst proportion of any that was tried.

(2.) When the angle of the sails with the axis was increased from 72° to 75°, the power was augmented in the proportion of 31 to 45; and this is the angle most commonly in use when the sails are planes.

(3.) Were nothing more requisite than to cause the sails to acquire a certain degree of velocity by the wind, the position recommended by M. Parent would be the best. But if the sails are intended with given dimensions to produce the greatest effects possible in a given time, we must, if planes. are made use of, confine our angle within the limits of 72 and 75 degrees.

(4.) The variation of a degree or two, when the angle is near the best, is but of little consequence.

(5.) When the wind falls upon concave sails, it is an advantage to the power of the whole, though each part separately taken should not be disposed of to the best advantage.

(6.) From several experiments on a large scale, Mr. Smeaton has found the following angles to answer as well as any. The radius is supposed to be divided into six parts; and th, reckoning from the centre, is called 1, the extremity being denoted 6.

(7.) Having thus obtained the best method of weathering the sails, i. e. the most advantageous manner in which they can be placed, our author's next care was to try what advantage could be derived from an increase of surface upon the same radius. The result was, that a broader sail requires a larger angle; and when the sail is broader at the extremity than near the centre, the figure is more advantageous than that of a parallelogram. The figure and proportion of enlarged sails, which our author determines to be most advantageous on a large scale, is that where the extreme bar is one-third of the radius or whip (as the workmen call it), and is divided by the whip in the proportion of 3 to 5. The triangular or loading sail is covered with board from the point downward of its height, the rest as usual with cloth. The angles above mentioned are likewise the most proper for enlarged sails; it being found in practice that the sails should rather be too little than too much exposed to the direct action of the wind.

Some have imagined, that the more sail the greater would be the power of the windmill, and have therefore proposed to fill up the whole area; and by making each sail a sector of an ellipsis, according to M. Parent's method, to intercept the whole cylinder of wind, in order to produce the greatest effect possible. From our author's experiments, however, it appeared, that when the surface of all the sails exceeded seven-eighths of the area, the effect was rather diminished than augmented. Hence he concludes, that when the whole cylinder of wind is intercepted, it cannot then produce the greatest effect for want of proper interstices to escape.

"It is certainly desirable (says Mr. Smeaton), that the sails of windmills should be as short as possible; but it is equally desirable, that the quantity of cloth should be the least that may be, to avoid damage by sudden squalls of wind. The best structure, therefore, for large mills, is that where the quantity of cloth is the greatest in a given circle that can be on this condition, that the effect holds out in proportion to the quantity of cloth; for otherwise the effect can be augmented in a given degree by a lesser increase of cloth upon a larger radius than would be required if the cloth was increased upon the same radius."

(8.) The ratios between the velocities of windmill sails unloaded, and when loaded to their maximum, turned out very different in different experiments; but the most common proportion was as 3 to 2. In general it happened that where the power was greatest, whether by an enlargement of the surface of the sails, or an increased velocity of the wind, the second term of the ratio was diminished.

(9.) The ratios between the least load that would stop the sails and the maximum with which they would turn, were confined betwixt that of 10 to 8 and 10 to 9; being at a medium about 10 to 8.3, and 10 to 9, or about 6 to 5; though on the whole it appeared, that where the angle of the sails or quantity of cloth was greatest, the second term of the ratio was less.

(10.) The velocity of windmill sails, whether unloaded or loaded, so as to produce a maximum, is nearly as the velocity of the wind, their shape and position being the same. On this subject Mr. Ferguson remarks, that it is almost incredible to think with what velocity the tips of the sails move when acted upon by a moderate wind. He has several times counted the number of revolutions made by the sails in 10 or 15 minutes; and, from the length of the arms from tip to tip, has computed, that if an hoop of the same size was to run upon plain ground with an equal velocity, it would go upwards of 30 miles in an hour.

(11.) The load at the maximum is nearly, but somewhat less than, as the square of the velocity of the wind; the shape and position of the sails being the same.

(12.) The effects of the same sails at a maximum are nearly, but somewhat less than, as the cubes of the velocity of the wind.

(13.) The load of the same sails at a maximum is nearly as the squares, and the effect as the cubes of their number of turns in a given time.

(14.) When sails are loaded so as to produce a maximum